Earlier quoted context omitted.
Except Wikipedia seems to put the barrier significantly higher, at 100 keV: https://en.m.wikipedia.org/wiki/Thermonuclear_fusion#Tempera...
A system of particles in thermal equilibrium will contain a small fraction whose kinetic energy exceeds the average by a factor of 10. Also, the energy available in the center-of-mass frame of two colliding particles is higher if they happen to be moving in opposite directions. That could give you another factor of up to 2. In any event, I don't think you want your fuel fusing all at once!
In addition to that, whether two nuclei fuse is also dependent on how squarely they collide. A glancing blow intuitively allows both nuclei to push each other away a lot easier than if they experience a head-on collision.
A graph of the fusion rate such as [1] shows that even at much lower average temperatures, fusion will occasionally happen when two higher-than-average nuclei collide head-on. As the temperature gets higher, this rate increases as more particles have enough energy and less require those head-on collisions. The peak rate for D-T according to this graph is about 70kEv.
I can't speak to why the grandparent's link referenced 100kEv, as it's been a decade since I last studied this and I'm very rusty.